In Old English or in Middle English, was "join" ever pronounced "jin?"
Indeed, join and jine were pronounced very nearly, if not exactly, the same in the early 18th century (much more recently than Middle English), when Alexander Pope wrote:
Good-Nature and Good-Sense must ever join;
To err is Humane; to Forgive, Divine.
No, "join" was not a part of the English vocabulary. The letter "J" was not invented by then. "Bindan" is Anglo-Saxon word for join. We still use this in Dutch(Binden). Even in the original 1611 King James Bible there is no "J". https://www.originalbibles.com/the-original-king-james-bible-1611-pdf/